The total harmonic distortion (THD) of a signal having a fundamental frequency is the total amount of energy present in specific harmonics of the fundamental frequency relative to the amount of energy in the fundamental frequency. The harmonics of the fundamental frequency are integer multiples of the fundamental frequency. The THD is generally estimated by determining two quantities: the energy in the broadband spectrum and the energy present at the fundamental frequency. When the signal is strong relative to any broadband background noise, this estimation technique is sufficient for some applications. Estimation of the energy in the broadband spectrum may be found by taking a fast Fourier transform (FFT) of a time series set of measurements of the signal of interest and summing the square of each resulting bin in the FFT. That is, the THD is conventionally estimated according to Expression 1.[Expression 1]THD=((broadband2−H12)1/2/H1)×100%
In Expression 1, broadband2 includes harmonic content, and non-harmonic content (broadband noise). The value of H12 is the energy of the signal at the fundamental frequency, also known as the first harmonic. Expression 1 works well to estimate the THD in a signal when the signal is strong relative to background noise, because the dominant contribution to broadband2 is from the harmonic frequencies of the fundamental. In Expression 1 subtracting H12 from broadband2 is done to make the numerator an estimation of the energy in the other harmonics of the fundamental frequency, although it undesirably includes the energy from broadband noise as well. At signal levels that are low relative to the broadband background noise (non-harmonic content), Expression 1 provides a poor method for estimating true THD, because a significant contribution to broadband2 is from broadband background noise. At signal levels that are low relative to the broadband background noise, the numerator in the right hand side of Expression 1 is a poor estimate of the energy in the other harmonics of the fundamental frequency, and consequently Expression 1 offers a poor estimate of THD. In an alternating current (AC) electrical circuit with a voltage or current having a fundamental frequency, low current levels may provide a signal that is not large relative to the background broadband noise. It is therefore difficult to accurately measure THD in an AC electrical circuit at low current levels. For example, it is difficult to accurately measure THD in a power meter at current levels below 20% of the meter's nominal current levels. The error in THD increases as the current decreases as the broadband noise typically remains the same.
Measurement of total harmonic distortion (THD) in a power distribution system is desirable as many electrical devices and equipment are sensitive to the harmonic content of supplied current or voltage. Non-linear electrical loads, such as the electronic ballasts used in fluorescent lighting, and electronic components that rely on rectifiers to create a direct current to operate internal circuitry, typically increase the THD in a power distribution system because non-linear loads do not draw current evenly but instead rapidly switch between drawing and not drawing current in order to achieve a direct current rectification. Harmonic content in a power distribution system can also be amplified by the reactance of the power distribution system or from the reactance of components connected to the power distribution system.
High values of THD in a power distribution system can have harmful effects on the distribution system itself and on any electronics connected to it. For example, high values of THD in the current of a power distribution system may lead to excessive current being drawn on the neutral wire. In another example, high values of THD in the voltage of a power distribution system may lead to excessive, and potentially damaging, voltage being applied to components connected to the power distribution system. In a power distribution system incorporating three powered lines with each line having a waveform in current and voltage and with the waveform on each line having a 120 degree phase offset relative to the others, triplen harmonics of the fundamental frequency are of special interest. Triplen harmonics are those that are odd integer multiples of three times the fundamental frequency. In a three line power distribution system the triplen harmonics are of particular interest because the 120 degree phase offset of the three different lines causes the triplen harmonics to be additive. So, for a power distribution system with a fundamental frequency of 60 hertz, the first triplet harmonic is at 180 hertz, and so on. For a power distribution system having a fundamental frequency of 50 hertz, the first triplet harmonic is at 150 hertz, and so on.
Additionally, accurate determination of THD may be of interest in applications other than power distribution systems where analog signals are sought to be monitored. For example, audio systems are designed to meet THD tolerances in order to improve sound quality and potentially decrease feedback.